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</div><h2>SL Paper 1</h2><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A researcher consulted 500 men and women to see if the colour of the car they drove was independent of gender. A \(\chi^2\) test for independence was carried out.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The colours of the cars were red, green, blue, black and silver.</span></p>
<p><span>Find the number of degrees of freedom for this test.<br></span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>At the 5 % significance level the \(\chi_{calc}^2\) was found to be 8.73.</span></p>
<p><span>Write down the critical value, \(\chi_{crit}^2\), for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(180\) spectators at a swimming championship were asked which, of four swimming styles, was the one they preferred to watch.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The results of their responses are shown in the table.</span></p>
<p style="font: normal normal normal 20px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_06.29.26.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A \({\chi ^2}\) test was conducted at the \(5\%\) significance level.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(\chi _{calc}^2\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The critical value, at the \(5\%\) significance level, is \(7.815\).</span></p>
<p><span>State, giving a reason, the conclusion to the test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The heights of apple trees in an orchard are normally distributed with a mean of \({\text{3.42 m}}\) and a standard deviation of \({\text{0.21 m}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that a randomly chosen tree has a height greater than \({\text{3.42 m}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that a randomly chosen tree will be within 2 standard deviations of the mean of \({\text{3.42 m}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to calculate the probability that a randomly chosen tree will have a height greater than \({\text{3.35 m}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The probability that a particular tree is less than \(x\) metres high is \(0.65\). Find the value of \(x\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Members of a certain club are required to register for one of three sports, badminton, volleyball or table tennis. The number of club members of each gender choosing each sport in a particular year is shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A \({\chi ^2}\) (Chi-squared) test at the \(5\% \) significance level is used to determine whether the choice of sport is independent of gender.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected number of female volleyball players under this hypothesis.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the \(p\)-value for the test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State, with a reason, the conclusion of the test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">Tony wants to carry out a \({\chi ^2}\)</span> <span style="font-family: times new roman,times;">test to determine whether or not a person’s choice</span> <span style="font-family: times new roman,times;">of one of the three professions; engineering, medicine or law is influenced by the</span> <span style="font-family: times new roman,times;">person’s sex (gender).</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the null hypothesis, H<sub>0</sub>, for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Of the 400 people Tony interviewed, 220 were male and 180 were female.</span> <span>80 of the people had chosen engineering as a profession.</span></p>
<p><span>Calculate the expected number of female engineers.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Tony used a 5 % level of significance for his test and obtained a <em>p</em>-value of 0.0634 correct to 3 significant figures.</span></p>
<p><span>State Tony’s conclusion to the test. Give a reason for this conclusion.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The producer of a TV dancing show asked a group of <span class="s1">150 </span>viewers their age and the type of Latin dance they preferred. The types of Latin dances in the show were Argentine tango, Samba, Rumba and Cha-cha-cha. The data obtained were organized in the following table.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-20_om_14.07.46.png" alt></p>
<p class="p1">A \({\chi ^2}\) <span class="s1">test was carried out, at the 5</span>% significance level.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the null hypothesis for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the observed number of viewers who preferred Rumba <strong>and </strong>were older than <span class="s1">20 </span>years old.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use your graphic display calculator to find the \(p\)-value for this test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The producer claims that the type of Latin dance a viewer preferred is independent of their age.</p>
<p class="p1">Decide whether this claim is justified. Give a reason for your decision.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A market researcher consulted males and females to determine whether the type of coffee they drink is associated with gender. The types of coffee are Cappuccino, Latte, Americano, Macchiato and Espresso. A \({\chi ^2}\) test was conducted, at the 5 % significance level and the \({\chi ^2}\) value was found to be 8.73.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span><span> the null hypothesis</span><span>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the alternative hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the critical value for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the type of coffee drunk is independent of gender. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A study was carried out to determine whether the country chosen by students for their university studies was influenced by a person’s gender. A random sample was taken. The results are shown in the following table.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-20_om_07.38.20.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A \({\chi ^2}\) test was performed at the 1% significance level.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The critical value for this test is 9.210.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span></p>
<p><span>(i) the \({\chi ^2}\) statistic;</span></p>
<p><span>(ii) the associated <em>p</em>-value.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State, giving a reason, whether the null hypothesis should be accepted.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The number of calories a person burns during a walk depends on the time they spend walking. The table below shows the number of calories, y, burned by a person in relation to the time they spend walking, <em>x</em>, in minutes.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to write down the equation of the regression line for <em>y</em> on <em>x</em> in the form <em>y</em> = <em>ax</em> + <em>b </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your equation to estimate the number of calories that a person will burn during a 17 minute walk.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether your answer to part (b) is reliable. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The mass of a certain type of Chilean corncob follows a normal distribution with a mean of 400 grams and a standard deviation of 50 grams.</p>
</div>
<div class="specification">
<p>A farmer labels one of these corncobs as premium if its mass is greater than \(a\) grams. 25% of these corncobs are labelled as premium.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that the mass of one of these corncobs is greater than 400 grams.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the interquartile range of the distribution.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A group of 100 students gave the following responses to the question of how they get to school.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.46.51.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A \({\chi ^2}\) test for independence was conducted at the \(5\%\) significance level. The null hypothesis was defined as</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{H}}_0}\): Method of getting to school is independent of gender.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected frequency for the females who use public transport to get to school.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the \({\chi ^2}\) statistic.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The \({\chi ^2}\) critical value is \(7.815\) at the \(5\%\) significance level.</span></p>
<p><span>State whether or not the null hypothesis is accepted. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A survey was carried out to investigate the relationship between a person’s age in years ( \(a\)) and the number of hours they watch television per week (\(h\)). The scatter diagram represents the results of the survey.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.00.45.png" alt="N17/5/MATSD/SP1/ENG/TZ0/05"></p>
<p>The mean age of the people surveyed was 50.</p>
<p>For these results, the equation of the regression line \(h\) on \(a\) is \(h = 0.22a + 15\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean number of hours that the people surveyed watch television per week.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By placing a tick (✔) in the correct box, determine which of the following statements is true:</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_07.09.18.png" alt="N17/5/MATSD/SP1/ENG/TZ0/05.c"></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Diogo is 18 years old. Give a reason why the regression line should not be used to estimate the number of hours Diogo watches television per week.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A market researcher surveyed men and women about their preferred holiday destination. The holiday destinations were Antigua, Barbados, Cuba, Guadeloupe and Jamaica. A \(\chi^2\) test for independence was conducted at the 5 % significance level. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The </span><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">\(\chi^2\)</span> calculated value was found to be 8.73.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of degrees of freedom for this test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the critical value for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the conclusion of this test. Give a reason for your decision.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A survey investigated the relationship between the number of cleaners, \(n\), and the amount of time, \(t\), it takes them to clean a school.</span></p>
<div style="text-align: center;"><br><img src="images/Schermafbeelding_2014-09-02_om_15.05.16.png" alt></div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to write down the equation of the regression line \(t\) on \(n\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of the Pearson’s product–moment correlation coefficient, \(r\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your regression equation to find the amount of time 4 cleaners take to clean the school.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The marks obtained by 8 candidates in Physics and Chemistry tests are given below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeEAAAA9CAIAAAAVo0a5AAARIUlEQVR4nO2dzWsby5rG73/SgoYBCQT2ZKOVZ3OYUbQQxmRxwQzkjCxwYDL4QmAWEjITvAgcpkWML4HAoYVNLiEzSQuHcJiQUHhzCDoUh4Fw0BScRQiiGcyg2/RCCFPULPr7S+6ubnWVnXrola2PX1e3nn7rrY/3D0RISEhIiFf9gTWAkJCQkFCihEcLCQkJ8Svh0UJCQkL8Sni0kJCQEL8KeLQsVcQhDnGIQxzMj3iPtmy6jEeDkE/M25w5AA8MzAF4YBAAPDCEAIRHsxfzNmcOwAMDcwAeGAQADwzCo7kT8zZnDsADA3MAHhgEAA8MwqO5E/M2Zw7AAwNzAB4YBAAPDMKjuRPzNmcOwAMDcwAeGAQADwzCo7kT8zZnDsADA3MAHhgEAA8M2T1a17oxU0MaXeUVQAYhhBATKnetv99R4FUBkNiExy2p0VU/mwV8mqWlDl/0e+d64guudO2ofzrRcWFfmVK83RPfJgNzAB4YBAAPDHRx9AKpu7JUkTcUeEWIOR332rJUkasH49mSEELwdNSuFefRjulvFPNxhBhTdb/ePAL6ctWr8AwM2vXO2dQs1adz3xNLHf70RtmrS5V6DxilAhjow3G3WpGlilzdG35A1M/ULAzYRBfj10p3YwCM8JXC+uSs15alSr3z7JfVl5seYCWDiYD2cthp98Fllg/MyrCiEZY6fNFv1mSp0X36c6aYI9etaIB+1Y3hdkdoQfEZRfjjcqYd1Nsqov0RZ2NIutwm+qjs1aWKLNVavRcwx62Y0qOvdO1hwDSd4Noxha/jziavcfRyph3U3cfJNd/8ZbzfqO9rsxJdOtd9ifVfnu7Vq3vD1xeI9tFCC2A17P5oahBCsP7hsPkdhTFlZcBIvXd/7/tqRa5G/XEybO4cghkmSx0ctZrHMHWbZGqERAY8He3sdu83ZGlrrR6d3AjYhMctKxzBMzDYaSmT9D+iHLficqYd1N1+Nq1F5vdoPNMeVOkBsjEkXW785e3T5x+R9bv4+bjTkHPcirQefQWHGxVZqsgdTSekaI8uUnimPajWUt+p2ACDutR4oH0pzaVz3JdzqOxkDRgLA8DTUbvmi9wXSN2lC+SzMyyQuhuxpxDAJeh9t61OU17H7I0Qy0AIIRip22v26EQAPB21fU9KA/SrGUJa+lvRnAzbj6NNkVV5PdqcDDuP+p1GSR5NCIm73Pj3ny98EWHW+2HdcfSH3+zOb7uvTU0SSmc/HOtXzl82u9pXQpb65FnX7SJ1NN2X3XYeAIQQbKL3w05Dliqy1HazxvYzyv/hYc2hshN5yunw/PWot2sbMZ6BQdvrnVldthzXOKto70tswuNWyv7BWgAuQW/LFyBcgt5OCXE0ISTZnjZ9powNMEjf570dHo2Ruh3IM6z7QWV/rQEGdanW6v04BvT5rhwAluZQeTSECPS22Hp0WAboV0v26Gg+2vFouXkE9IUBBnXPNLE5PetWK7JUc++VK/jsT5Y/GqBftf6OTfR+qPzkj8odj3Y+oa0ifAl6W85HXXoXw0QflZO3UY+2432/fTsfLlXk5jE0/w8qO4EMmp1bp0yoUShHGLvZ6v1oZaLzpINzPSSkSr1zNjUXOlD6GbOfORiS7Mn/S7CMI+11vBUeHf3LZSbDytOjckKlWqunlZ52I4RgE550lYmZ8ZTzM6Ty6I0MsVQ+j/aOdl9950uEB3IdV1C5I1Vk6e4QWqbhDDnad88cnr6zW9CKqZuDMfJ3kUMe7fdlO1X9QPuC7Zc5AXus7Jg9FGLb5iJLje/3j/4cnsphfawV5pchuvsSI3Xb61IYU3W/Lu0M4bw0AEKIrxtUSx+sFcEQNaOoI3+DHh21p1I82hLW4fmP/WZNltKnFosDMCfDzgk0cdZTzs9w3eXGBni8nWNUgDbXEdZqj3bHfGvb6hQbn8YX7vnMnTC20VXeO4/foEfbsXDUNF2rrdQ7xx9RTCLUJon5IVm+H5tALzu3TnVfYgMM6v7zsmIZqlszV/CCzofKD/1mTZbah4B+qFV4dHYGzjzakpU5jGuWdQLM4dMfnECVM4/2Hh6UAGV5tBtKN5+8OX15Ebh+7lShijPvLejRzpyeWNN051rJzgSDAHeiR2M7IRNzLW+ER6fp564VgFg5qAf/rM2wm9OnDOSzM4hcRywAo1xHSBnTr7kBsAmfH3qD/Fx59Bw+PYr6UiaA0jzamROT1Cm2f+TWW4Ie7Wa7EuevLHVw1Ip11aRchxf9RX/DNyLXETWgBVJ3S42jw2N0c6jslDXpKsWUhowNcis8mmCkbod7V5vrHzMMCk9H7fslzo+2+8SRgzL/VpxHL2fnz88yGnQUIOMalqQwzbHReg8Yboga5rbSGkFP1H8aKhrUl8FZzI5H2z8wL31sz8k3EQDIJF/fKidjqGP7ARA3Yc4Gc0Yv3dzIvjbD9knVe8DAOrxwBtxuypihAfqBU842gl8QQI16HkU+BjH3LgGA1dw7vwxwOChnCmasOImjlzp4fuxl/4zp6YuLdH3c7B4dWQseCVd9s+Wkza7yJDzZzncy90LLQ/RPAP0v0gYtqSI3e2dQx4FPc7/Ly4fI1b2hBnVMCJldAGQgzUqGJizjtozYakF3hpAz7mx+HnUa4ffemLl3/iUkS33yrNvOME++CIA5VHa8FJP5edS5Sz2vvAiPLm8NyyoGth7NYg0L1uHbc+hNh+0p1yzoLRogKB482rA9zX/QdulSxtEFKTBaWJKsHEvqtRU3aw2LuxQ783rTYgCwDk979r1Y2lrwwJrjcH/WmTKfdwEuLUOw353RKQpqBHeyTVLgUgSAT1j/cOjGTznWu1IDBFWmR8de7uCSy+yJl/I9ejnTDurNY2guZuevUkb7xQPc1rXgtwKABwbmADwwCAAeGMr3aCu5/HCMPo1UWNw+dplkTNX9O9eumb6peyrdeAAeGJgD8MAgAHhgYBBHW5Muyve+MIbYm5RXAB4YmAPwwCAAeGBgmo8WihPzNmcOwAMDcwAeGAQADwzCo7kT8zZnDsADA3MAHhgEAA8Mqzw6bh64OMQhDnGIo+wj3qOjFi5Ugpi3OXMAHhiYA/DAIAB4YJBFroM3MW9z5gA8MDAH4IFBAPDAIDyaOzFvc+YAPDAwB+CBQQDwwCA8mjsxb3PmADwwMAfggUEA8MAgPJo7MW9z5gA8MDAH4IFBAPDAIDyaOzFvc+YAPDAwB+CBQQDwwJDHo7GJLsaqs4eO1OgqrwAyiAHBr6Z/97v17o5vTobNGstVi1iHp4/7ibtLfx33Hp/BDMsVebsnvk0G5gA8MAgAHhioPdqqmOfuIEqIVwPF2cvf2UV6rR4dW0AgXubkz+qvBZOYn0edrdbgwwoPxvqHw+ZWV/2ccnMS+nvCRB+tgrPJ1cLWAIBNdDF+rXQ3ottyGgicv1H27qTdZZCOYQWAq+VMO8i0mXXGRkg8U69WfbhKZ9EMJgLay2GnHdkEtZyr4FfcLvtll20LYdAX2CzoKtDz0Hm0a9BHkZ1h51B56NhlKVWm0sbRc6jsFEySele8xJoDcaK8Ly0Yux2WOjhqlVJEDiP13v2976vRgg8LpO5/3/ljXUq/EywNQzKA7zVW0Z91eXTymZr/PT79pGNCsP7L0716xiuSgQFPRzu73fuNSCWNkq5CQIGNUnNZZB6Pdio9WQd9jY4irkIuHhqPvqbMlZ3rIOVXAkyW/VAplMTaFjZlyb5L0NuS022ISndfhncWD1eKyqDsAMm1E/F01K6t3x1WFm80J8POo36nsTaPJoTEnuni94tP3vM7e1m/rAyJxQRKugr2lxng5HGg3PAl6D0ssVaWpTlU9uju/5wMCVeBnofCo51CWdc/ClyP/vCbvfd8u69NvS6/1zf3dh93chcVWdofgXdDu594BHTT2jBP9u2Z53uxXeHF61q6fzSnY6sKrX1sdrXffLnyyV/R+2GnIVcHYPqf4ZIxdtGZuGKG5mTYrAV8wURA+7HffjSeLSMObtd8SRNN5Aheal6VDQP0V/X9iwXg2aPnUHk0hCjrRu9FeHTw/0jdzlIIhoKBD49e6uiLP62HkbpdUsk0n6xYvtkbabmKDFAwxF+FHDwUHu1UFwxXbo3KeWXzCOgLp6qh8y6rMFX1YDxbYqRue7VO3GdAo6t+NvGX8X5Dlir15t2/r+6PPr3uB0J4p/qt/bG+mgsm+qicvLW+6woON4Kjl27FxfuP3/yqI3VXlu4OoWFOz7rBLsIVfPanuByF/XiwyuAGmsUydGsLVu9zMFK302XlaO9Lqz6k1Wgz8G+DY9p9VW+RR2MTnnSViZm9GEehHm0goPY7T7KWjLqZHh3SAqn7ZZVM83/prheWZR8JyMMQdxVy8ZTh0XHVwZ1CtJbHWR5qVxkP2a4zP8QulBfKn4RebP03GK2TOI8O1rH1lU8OldOdw9N3cT9s53s9jybOmIDryyZUHnldjfiS5DGi/2FYSc982TcqAF492pwMOyfQxBQFkwrzaC85G7kti2bg0aPxdLTzmK4/lxtgqcN3I6sPnbEHk4dhRV1wOh4Kj3ZHJ9PnOqIeHagkG0gvJHm07YarPdpX6ts/sSHZo5N/VLVtdYoTKy7aVMG32zD2t2A0PvXNNbE9+vr5JznuSwNpJ0PlX1vxw7lpdVs8eg6f/uAMALCNo90pT9kKY94Cj8ZIvZf9ewsEcHq0NDV/6RiuKzGcmYfCo50Q+PobLoVHx/xs8ng0Id7voeLVqE726LhRRCeUbj55c/oyoeLiKo+u94BB5lB9GXhUrt2jjan66F+0L9gt+kkbO9wKj8YmfH7o3Z+MPTrVC3Iz8OfRC6Q+zDNwV4RHE+vqU5w+HUOKMvDZeCg82p7mlRCxL3XwGth2ucKj3ZRCdKpDXo92MI5a7suyefR1E1f83xvIdbhJ6tcIvhyF5nusOdeBkbrt79mYk2Fzs6wJTxx6dNwU3SyTwIr3aLJA6u635dH5Eh0FANhaIPV+SfOjU3l0Nh4qjybOiF8wpYB1OFYOHriLNdxxuR4wvOjbpndnC9qTNLAO31mLYdz8um8Y0I24A59JfB5t2dPXt8rJGOo4NCXZ966/zj5d/L6IfE5I1vjbqmSOPQYY69HNvX6knO6axwyt5vUDX4Led9+wR4fEQRxNLkGv/U3lOnImOvIDOLoEgx9Ky4mniqOz8NB6NCGEGAhoI29am7MW3JY/47zZVZ6Ep7URbFqT3uz3vkfh6XQVeePJ+NVDNwi6o7z6D3u40p4+EXyxAq9mFwAZSOs3a/75fIRgZ8JG+xDMcCgbHvRZ+w1Ivbd6cYrl8kFfcDw62r1Y/9y7wFoebE7PuhuppmMXASA8Ou5M8Zfx/lar9wLqS6tjt51xx4Ib7tF5Ex30AFiH5z9BazwG6788HQTna6+XIeYq5OPJ49G3Womjha6sGdCBi3EFlTvxq1rWvoaF+BPxZa4FDywq8z+E3J4TzUKvDAyJAH6t1aOTztRZjitV5OreUMuyaUtmhmBuxzvTsq5CVHg62j+hnk2RCwDPwKAdFziumyHhKuTjER7t13KmHdSbx9BczM5fJYwW+mSvBX/xX//+x5YyMZOngpaxFrw4MQfggYE5AA8MAoAHBuHRflkDiQ/H6NMoklCOl/l59E9bf/c3Fbk6ALNJ7LvK21OpIDEH4IGBOQAPDAKABwbh0X7Zs0Gy7XSK/+cv//i3svQPCSsUxN6kN5KBOQAPDAKABwbh0dyJeZszB+CBgTkADwwCgAcG4dHciXmbMwfggYE5AA8MAoAHhlUe7Q1QikMc4hCHONgd8R4tJCQkJMSVhEcLCQkJ8Svh0UJCQkL8Sni0kJCQEL8SHi0kJCTEr/4fsge2ZLNoNnwAAAAASUVORK5CYII=" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the product moment correlation coefficient, \(r\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in the form \(y = mx + c\) , the equation of the regression line \(y\) on \(x\) for the \(8\) candidates.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A ninth candidate obtained a score of \(7\) in the Physics test but was absent for the Chemistry test.</span></p>
<p><span>Use your answer to (b) to estimate the score he would have obtained on the Chemistry test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give a reason why it is valid to use this regression line to estimate the score on the Chemistry test in part (c).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Applicants for a job had to complete a mathematics test. The time they took to complete the test is normally distributed with a mean of 53 minutes and a standard deviation of 16.3. One of the applicants is chosen at random.</p>
</div>
<div class="specification">
<p>For 11% of the applicants it took longer than \(k\) minutes to complete the test.</p>
</div>
<div class="specification">
<p>There were 400 applicants for the job.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this applicant took at least 40 minutes to complete the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(k\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of applicants who completed the test in less than 25 minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Tania wishes to see whether there is any correlation between a person’s age and the number of objects on a tray which could be remembered after looking at them for a certain time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">She obtains the following table of results.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the equation of the regression line of <em>y</em> on <em>x</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your equation to estimate the number of objects remembered by a person aged 28 years.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the correlation coefficient <em>r</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Comment on your value for <em>r</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A factory makes metal bars. Their lengths are assumed to be normally distributed with a mean of <span class="s1">180 cm </span>and a standard deviation of <span class="s1">5 cm</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On the following diagram, shade the region representing the probability that a metal bar, chosen at random, will have a length less than <span class="s1">175 cm</span>.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_17.53.42.png" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A metal bar is chosen at random.</p>
<p class="p2"><span class="s1">(i) <span class="Apple-converted-space"> </span>The probability that the length of the metal bar is less than 175 cm </span>is equal to the probability that the length is greater than \(h\) <span class="s1">cm</span>. Write down the value of \(h\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Find the probability that the length of the metal bar is greater than one standard deviation above the mean.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Minta surveyed students from her school about their preferred morning snack from a choice of an apple, a fruit salad or a smoothie.</p>
<p class="p1">She surveyed 350 students, of whom 210 are female.</p>
<p class="p1">She performed a \({\chi ^2}\) test at the 5% significance level to determine whether there is a relationship between the choice of morning snack and gender.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State Minta’s null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">150 students showed a preference for a smoothie.</p>
<p class="p1">Calculate the expected number of female students who chose a smoothie.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Minta found that the calculated value of the \({\chi ^2}\) test was 3.576. The critical value at the 5% significance level is \(5.99\).</p>
<p class="p1">State Minta’s conclusion. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>In a school, students in grades 9 to 12 were asked to select their preferred drink. The choices were milk, juice and water. The data obtained are organized in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.06.16.png" alt="M17/5/MATSD/SP1/ENG/TZ1/06"></p>
<p>A \({\chi ^2}\) test is carried out at the 5% significance level with hypotheses:</p>
<p>\[\begin{array}{*{20}{l}} {{{\text{H}}_{\text{0}}}{\text{: the preferred drink is independent of the grade}}} \\ {{{\text{H}}_{\text{1}}}{\text{: the preferred drink is not independent of the grade}}} \end{array}\]</p>
<p>The \({\chi ^2}\) critical value for this test is 12.6.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(x\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the \({\chi ^2}\) statistic for this test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion for this test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A shop keeper recorded daily sales <em>s</em> of ice cream along with the daily maximum temperature <em>t</em> °C. The results for one week are shown below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the regression line for <em>s</em> on <em>t</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your equation to predict the ice cream sales on a day when the maximum temperature is 24 °C. Give your answer correct to the nearest whole number.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The scores obtained by five candidates in Mathematics and Physics examinations are given below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the correlation coefficient, \(r\) , for the examination scores.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the regression line, \(y\) on \(x\) , for the examination</span> <span>scores of the five candidates.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A sixth candidate scored 72 in the Mathematics examination. Use the regression line, \(y\) on \(x\), to estimate his score on the Physics examination.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Identical mosquito traps are placed at different distances from a lake. On one day the number of mosquitoes caught in 10 <span class="s1">of the traps is recorded.</span></p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-18_om_17.36.55.png" alt></p>
<p class="p2">It is believed the number of mosquitoes caught varies linearly with the distance, in metres, of the trap from the lake.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Pearson’s product–moment correlation coefficient, \(r\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the equation of the regression line \(y\) on \(x\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the equation of the regression line \(y\) on \(x\) to estimate the number of mosquitoes caught in a trap that is \(28\)<span class="s1"> m </span>from the lake.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">\(200\) people of different ages were asked to choose their favourite type of music from the choices Popular, Country and Western and Heavy Metal. The results are shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was decided to perform a chi-squared test for independence at the \(5\% \) level on the data.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the chi-squared value.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether or not you will reject the null hypothesis, giving a clear reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A questionnaire was given to all members of a school community to find out which drink was the most popular to have with breakfast. The results are given in the table below, classified by age.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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lpCfv8k3tTs1kvlSKDOtx/ep3YQFZLap95DHn/GyNd5Mk11q//yn55jbtCx30P9KtWd2HfeDY23aWPmum129WBX6XcDrZBPc1ALNHasI0w78a41w3T1KF3gSA/uO++NR29Ac+QGu/Ybk+rCzaF9kvOS5mimOdIKAzRHDNAc2bAeNa37T2zju6F9wtfLv0nNQYUCX2zgw4ZcczBZwJtfOrbCv94yHUywY25UB8j7DfXWgoLRG7Kfi0U0EumrCbiw6CEv8cl4JmO8wDzeQR+HPuw1wz7j54OZSp7YilxzRMfRTAJBRq3n23sW7aBEhaQJzKyQ/LmCEgYe3xo7p2F0mT6IbLko320zqwdrMEFXUiS2wr5L/UIv3RravqDA9M5aTMf17NMXQhOMUpmPCy5pC2gOEXrWT9AcEvgSezBBxb790z3+78uiOYJkgvyxleKaI7lPQag5Yu0zjKFEDnr/ApqDPabvoLHxoB9dX5Fpjki0KDzuTlw/uePmazXHfGbt1mkSu5DAR1tj5/+8g58P2MKsqJDcCr6DzNGPvTv1THGQTH6mKz3lSqnRMd45vrguyG+bVT1Su3sKaI4wahMe1JKZBaa5zOVKqVxvj94rzT9Q3kOdF+yhQXZuvOySpmimOSC2sgDQHAuIVir/cDR4zSerl0ZzhIs2sqk2IV+lOZIfFmqO2CDEvpUlhgppDprxUN2dzH6Pf1ISW+H3TPYFqd/6Os2BZ9bOte54umhoZPKo1vzrs72nH/inRYUkPAGisWMdzeULEjGCnJtyvb03zZAduW8b93hqUeQcmiOzLWUXOEy4qeaw7dLQooc6F9gxNwSjoOSSnmimOYJFXBz5zHXIIQ0AzbGIU8fcqveQl3hrTvRQ1EJza44wNp8RqcXuwR6aEUKWElsJ217WIBTEFNJiqIDmYLPhjNgKISwrh25VrW4PLZ4SGSY9sAySoEyC2Iq0kYg0h384bN0NB0V89CbUEwnS+ROyQrK5fp4gSBo8Q4NWlooqctt8sRXBKn1Mc/A1ElG+i6jAcxfdbwplzSrQo4c6B9hDP97Lrs+SS5qim+aAvbJyQHMs4hj1Wlmd4SVa5yAkTFSsbg/3HdZzY9e2jJ1uMH0MRrgB8nC4OsJaVCwhIx4OOI0MV7uT2Ry7B6P2zVisJJGywAgGWvbaD+zaf7NdHI5DtGryHNLMQTQI0LRMxzscUnkR7kz5PO4+yFwoZrkLwQQau/bPtosJ8elNaErj7OBh9w/poEb2rSTvWaKHtKXR340LWEEhg5jL1thxeQAiGJLjfgxw3w4Ny3bnzOxJHUMioZwct+XVgw/5XPl1rRmeuwePOjdrkShJAu5Q+rCBodiixdy1ke3OBQX+8sZ4NKGVZGbtVMVKZfno0UPlYe7ab98wvT13D3/q/zfPpJZduhxopzngnWBSQHMkwUeT7hrfrzd30f2N7EXoS6Y5CN0GOWGp6XQYo+8+Z8TC6u0Hw+D95aXrHevXaGLBDcM+i7zfmg/wwXbHRufhgf3y+47xfPLajgUyoiqEEdnLGuihWJ7H9tDYFnyX3YHJqfXeGH120H2+XXPqh1stwiOSBBDZppvIGODn6+3Hn+znO23jlfXWzkzIyEhJoYN0kIsQPeTV5dQxu6kRNLOQkbfKmmjqvLsX2bkaT4+I6CT3I3J+c6xBsxTbBBv7rZy3TVaPL4RE9vRWt0eHH1917w5fWm8yfiW2PZhJlnA/cMRB2QWeHSDHc6z+ei2xw3n16NmnZ8HWhNKtXnrpcqDIC4l170TTDrZuqayi+tVPPtlQGiCQoMhiwdbFxGJ8gsunOa4gGZpDz7pOCCEER7JHgUsANDcdAC+IAMsUBSwmBzRHDuj7LRKaQ6u3o9KFNePQl2V7ADoCzU0HwAsiwDJFAYvJAc2xiIxo64lt3Nbrb63RKFX7pWM/H1+qdzEB0Nx0ALwgAixTFLCYHNAcC5m7tjWMrnOs98avRdEyRbBNGeEfzwMuC9DcdAC8IAIsUxSwmBzQHACgEmhuOgBeEAGWKQpYTA5oDgBQCTQ3HQAviADLFAUsJgc0BwCoBJqbDoAXRIBligIWkwOaAwBUAs1NB8ALIsAyRQGLyQHNAQAqgeamA+AFEWCZooDF5IDmAACVQHPTAfCCCLBMUcBickBzAIBKoLnpAHhBBFimKGAxOdmaAw444IADDjjggGMZR1JzrFj4AMCVBZqbDoAXRIBligIWk1OB2AoAKASamw6AF0SAZYoCFpMDmgMAVALNTQfACyLAMkUBi8kBzQEAKoHmpgPgBRFgmaKAxeSA5gAAlUBz0wHwggiwTFHAYnJAcwCASqC56QB4QQRYpihgMTmgOQBAJdDcdAC8IAIsUxSwmBzQHACgEmhuOgBeEAGWKQpYTA5oDgBQCTQ3HQAviADLFAUsJgc0BwCoBJqbDoAXRIBligIWkwOaAwBUAs1NB8ALIsAyRQGLycmpOXzbuCV7ffo1wz5bVZG/Hc5c6y634a2h7Wd/Crv2016zVK6UyvX240/ufLWFpMxd2xq2v5+4MTdj93Cv16qUypVSq//00MVL+33s2pbR6Vpu/KzvvBu2G5VSuVLdHu47AgtqzaXqoTxnf9SpliulcmW9t2cnHI49NKgHfULLdJZXHy4aVV7A7ocRrcDrg4njJS97qF8NutmtsXO6+hJqUD/ltW7u2s/667VKqdF5+GGJXVBulFrMc9DrV8b2jR5KVqZgHKluj5bZVS8kv+bo9q2pTwghXybt65VSuVK6O3HPCJm7h487DdAc5wQ75oZMc5zYxmalVNswP8+su5VSbcOcrra6eA4y++u1iMc5/uGQnadHY8c6EpftxH707DyVxHeQySRXpR3VHNi3R81Sud5DHrNSo2N+vnSyQ4M+PSfz2evHIyrssPvp4Xa9tDm0T8Lr+GjSbfDKsPqK+lWo8YL/z8nTjy7m9qwOkBe12Xxm7SrXcKrrp7zWYd8eNdfvI3dO8AwNNpvGofIeQJ3FTh2z+6f27TrrFaOc2Mbt5mDfxQS7+/fWb8da7mrJqzl+QTZ/hoTmIITMZz+//QU0x/lwrY5Ec+DpuFWrlK53rCMPDZK9/PI5s0d//P57NsmIaY6TX6yXn9w5Idif7tEP3BAqT+zbo+Z5FsN82+j+pXennqE5jlFvrVK63rG+kEC6VXcnMyXrQOdHdZ+eG/zvg4Mv4aiHp+NWLdK1Yd8ebaRnV5cEFV44/dfBx1lgUA/1q2t9dBxe9w+HrR/iKkQBiuunvNbh6bh1MzSah/pVNatBUVRbLNEwCaHdY6hosYcGdXXLkOfI50hrDuArkGuOM3t4rRyMrIoI1sxFHqdVQrTOwUXJ+QNwVF7ENQdbduaWSfz38nBpNEeSY9Rbi3Rt1EetvmmhdIxAe5R7ATvmxvrI9oMGRBtdrdl7MkEqg4bKLRMnVuuwY27EQk7HqHdT+QKbfprj1DG3YutkSsXZBWqOSHA9FnXLPB8miNz4q/W/LF+hxcM39FsHr4xtNsFNhPF8531wiR98kh0E/2rN3jObZj+wkZsO7TP6AeqVMJ4qGVN9B700+Fw/kbgQiTUms1tEBomkQawPJuiJUHOExeazfPGDxH6u1OqbyKH9V/iV6x3zHbdb6x6anbn792hwpNodT2XjxJlt3BDZh8U+or6L4jnWoFmKP4WktNnw2hLVHEyrcZHBHzO11hJU1+DD/Ay7W1aFoefRC17CXHWJr/1Gf2sxmvXp+TlGvVagMnmIkLeR7MqgL6pj8Ga//QBFU7XYAmeZVz9L2kCWiGb1M1rrTh1zqxILSB2j3pryRCLtNEf6jIf6VWXRz4vSHGwuW+9aM0yrAl3lFp2PNKr1+8g9TcykaRdW7yEvDGpyXcbCxo0d6wizlILWPUQXKb2p2a3TS9TQXYte4H1i40+9F794v45btco1wz6L1FHfeW88epMeU2k5qwPkYTyzdqrRWDUrW71rzTBLvKAxsxwPvtZHx5FRSr7OEQ6lggchrGzrI9tn5ay396Y+jnyFnjll9qzebN5c65j7E7qEIG2oQs0RVUWZSXCEhIohss4hKa3sDlHNkbAM+29WQ/I/j6l0CJ7xzB7t0oohqjCnjrnFfcTTFPjXBS6gE1NaSz1n//Hw9TetOTzUb0Xn5YQQgl37DUu+WXUQ8CtR5oUwSzRLqGHXfv2kv16rlGqqMhX0qp+xWpdWGKA58imMb0JzxILrdIi6YdhnwvPhfeh/+ajGhl42JlUHyMPJS7Gky/hoxBowLRi9xMdyNi2mhj51zK16D3msDNJpGRty1vroODnOcdkUfwT666IH53GKQJ7niq1Epu/ZD8KiD/GC8fBwfEmAl5NmXPK9M9LAR451jnIl+lDxT6Q0h7S0GWRpDiYLeA4HM1T2TXidoVexb7+cUP0qrDBcTfaQly5/tguoJQtPSfXq0/NyYhvfiVQFdvfvrScjypqj1gt84VMQncQzNGgJGtfS0al+JmodaI4srormSEQBMmIB6dV1meZg+A4yRz+yFMLFmoPfJHrwJW42TiTGJLb3oVIq19uj97I4tOegveFfe7FkSYnmED44HymTA1hRzRF/kGTaR8y2As1B3ffVmiNmxsynSI3Z8tJmkKk5oruIG53eblMoekiYEdIyHXx8YH30Ys+VVWHoczlobDzo02WSpMtS+ibYyFNk465OfXpOsG//1JdtEcIeGqR2YWiNei9kpf6FpDNMV4V6yzDStQ5iK1lcldiKaGVbsuK9QHPQKHtjxzqaJy6JYyv8JlnZMeKhPcyuyE5rYJkH9a41mycUgDi2Inxw0aRZvm8lrTnin1esOQgf1DPzkpamOUKokpNt1uVSdfPHl8/2Do7jz5VVbJozVN2dzH4v4LKoDMq3cVebPj0vePZ29HTBo2HH3FDd9RdCAy8EC2ZZ4Om4deeqvp+DEEGti2/HoFa6DjmkmTmk0TOp3NuVckGagw+NQf7EgvOR+2RpDj5vzoqtEBJbz6+3jQlPzwwC7Rljj3xoJ3MX3W9mDntM1mTFVgiJvb6iuj20gqKIHlwUWxFNYlLjcfaD0CGfS5xEoGEJmgPPrJ1qdFj1beOWYIYhiq0ISpuBXHNQ3wWZNAJSaRlEVmGogpTHVoSvcaPBhZz7dDTp03OCXTR6iLidsT99OT5Iew176Md7Kibl50YDL8RycpN46N5ATaxKA8uIax3slU3zDe6VDROqo94NMj3ZOIRd+2+2i4XnI6NyD3nhbsx4xKS0NXZc2vtHunjsT/d2MltgMK6wFYu5ayO63SAe0Q/48sZ4RCULHUTTbZ4Pt7UN81ePB2JCBeB/HncfZK0hix+ciRiatzg7eNj9A1vVz1pFiFmJiB+Ep6y296b+GXtZVjKHlGqOwNTUfUFWhGQlPJXGG00KefiBvWemdVew+SXyEydHBwf/xtLSZpAlFwihGXbPh+1GvlcQUiEbX3kSVZggNNYyHY9HTLiGELjgzH39iIlOfDTpNrJ0dgY69On5wL5j9WNvgQuqxNy1375henvuHv7U/2+p/tMPBV7AR5PuGt8PNXfR/Y1IE8Cu/eY1Myh2P4x6BlLzAmLl9VNS6wiBd4KlyQ7SXb53glGi7+pOJGeQ2K7RWDw783z0ZerXO8aDTnjPuxN3zl8z1eqbaOq8u0czt2l2XmwXGT0aHeMdS9yLbKMNUzRi2RXRgP3sADkeq9OCt3ezXQ+1Zs9E01/RgO9xdbxwNI0ckbwQkUHCbaL19uNP9vOdtvHKemun+xTZXtlyajdmdPdpxCCxr9waWmZo6msPJi/uxu6fdnk644EOvZE3sldKrb75c0b50zYMlyIEpU19M/3S/VjAaL03zjRdJng63vwu+dKwzArD9rOUK+u9MfrsoPvhXm6hC87cg7873nTSa6W23cpQ3afnhW/aih9MBbJlQrru+Erp+yTOhwov8DqWWCIlhARLZfTSywNVG2WJ6voprXWUuXv4mA0WS/3zC7lRZ7H4Hx9IRE+CPZIZ749fKeeIrWIY5ssAAA0wSURBVKgmQ3OUFb1rOUNzZEzHAV0Is0f1QffmdjUAL4gAyxQFLCbnEmqOyMu2M6a/KyZ490N6JQDQAzyzdqqbQ/sEz97tZSQfKEb75nYlAC+IAMsUBSwm5/JpDuyYG6XUHyZQEqDKiJyd2MZtHWKKAIcGBK93rH/a5nNb3Rq1CM2b2xUBvCACLFMUsJicy6c52J81D9c5as3ekzdqAlT0L7xH1jnWe+PXSmNlQAoWGl/0fndV6N7crgbgBRFgmaKAxeRcQs0BAN8Q0Nx0ALwgAixTFLCYHNAcAKASaG46AF4QAZYpClhMDmgOAFAJNDcdAC+IAMsUBSwmBzQHAKgEmpsOgBdEgGWKAhaTA5oDAFQCzU0HwAsiwDJFAYvJAc0BACqB5qYD4AURYJmigMXkZGsOOOCAAw444IADjmUcSc2xYuEDAFcWaG46AF4QAZYpClhMTgViKwCgEGhuOgBeEAGWKQpYTA5oDgBQCTQ3HQAviADLFAUsJgc0BwCoBJqbDoAXRIBligIWkwOaAwBUAs1NB8ALIsAyRQGLyQHNAQAqgeamA+AFEWCZooDF5IDmAACVQHPTAfCCCLBMUcBickBzAIBKoLnpAHhBBFimKGAxOaA5AEAl0Nx0ALwgAixTFLCYHNAcAKASaG46AF4QAZYpClhMDmgOAFAJNDcdAC+IAMsUBSwm53ya49Qxtyot08HST7lWh79c/YZhny0sS/j5uxN38cdXzplr3eWvi781tP3sT/nOe2O7XipXSo3Oww9uzESesz/qVMuVUqNjvHN8ufm+FYpWgyvGpeqhggpcrqz39ux47cau/bTXLJUr1e3RoXu5KrdyL+CZtVPdGjunkXNz137WX69l9SSrQ7lliIf61cRf66htmFNmj6DWadOpqrdYHOzab14anWq5Uh0gTy/75NYceDpu1SqlRAuRfDLnYIM9NKgnNQf27b2xaIBfOdgxNySaAx9Nuo1o22gah/xz85m1W6dG8w+H67V615qprwAroVg1uFro1kOJmc9ePx7tOz4hBLufHm7XS5tD+4RfPbGN283BvosJdvfvrd+OXLoEKPYC6zeiPSr27VFz/T5y5wTP0GAz0pOsFNX1MxgUokdgqBPbuMMEmf953G7o0KmqtliUuXv4uFNtdIwXyPFUF4ZxDs2BfXvUTA6oIr5M2tfzDzZntnEjoTn8w+F6S7iosHrYrD1Tc2APPfoBzTCh3W4ttmZD1fo1agjfNm5VSmt9dLzq8quhWDW4UujUQ0nB/z44+BL253g6btXqPUR7MuyYG+EsCntoUF+4DqoTSr1wYhu7f+ndqUc1B56OWzfD/sFD/eQqyIpQXT+PkTFC7jw84aH+Jqta8VpH14rUd6qqLRaAfXvU1G/R8Rya4xgNbjdv1iqlPGs1X6c5/M/jdkMWyFg9Ms0x/839nZsjsWbD/8s6Yqo5rs4YDJpDiDY9VFGOUW+Na45UsFXdGHk+1HkB+/ajjvFxhgZRzYEdcyO27HGMejfDgMIKUb0C9Jvzr+gE/dQx73A7pGpdXAerQpcW7R8O19d2rCOtBAc5h+bAM+vPg58/mVuVUjl7ph4G2Fp96+04HGwi+RDXDPuMjUPRoSiiOea+Y/XZUkEkyYMt6tIz1zvWl6wyeg56MWw3WHSj98wOZXIkIB0c1/jPh6kYrf7TUBxi93Cv16qUypX1wQQ9EWuOGOxZWJM4dajF2pZLSKA5+H/DL0VSRujV4EygwzILiX3n4JXBLROJtXOTlivXDPuEfpd6jS67RX8rw9s5bnt/8pFGnWvNnhXGU4XVIJNYosAYOT4hgVKJ+JqfYaXFvvOOOToo25k9vBbk3MzobZV3QxJ06aEKc4x6Ldajpft6D/WrNSVj5PlQ5gX/cNh+ZPtnXkxznDrmVnxGd4x6a4tT6JaAXvUTT8eb301mtD9P20SZlaLoYbFTx9yqrPfGNJNDm2QXUlxznDrm3T46xjNrh44QSQezwbXeQ15kVOODDR9r6TDPk4OyNMdZ5L/BAI8jLdNz9h8PX6c1By3AWh8dh9kVrJA0o6Jc71ozfGIbm5VSjUagCeFrKtXdyWyOHXOj1Ij2p/yGgeJZqDloMfhNkiIjbocY3tTs1mMxS99+eJ81M0EhaZYJtTl9xkqi/yqVK9Wt/st/eo65QQ0ejgrYd94NjbdpzZHrtqXWPTTDzJWBCpRXgwT05jRUR//d6Jif/eB5o9Xs7B/j+9Rl2J/udarUm7SP3qVW4jk3jT/1Xvzi/Tpu1bLsrAt69FDF8VC/NbJpL5ZWGKA5cnFiG98N7ZN4z0a0Gk21qp/YMf8YSlvaySRWg9aUTzC0sBiejlvX+XybdpV5ciFWQUHNgafj7iPbx6wNxAYhQkggI4L1j8Sienys5VPS3JqDTvrj8+kkXFj0kJf4uXgmY/y3eOyDagJasGuGfcbPB3MOWWwlbqhWNEs0v+YIy8kaj2/vWSx8KSgkYRKwOkAeFhiNeyqIE9MHWR9MxLlFuW6b6coF1SAO+zC7M1MM3OBcQGzyrvnJXrRf5iqHFo/dn/mIjnmnjrmlvBuSoEUPVZhgsCSEgOY4H9i3f7rH5iSgOfLAZrzhCQ/1q+V6e2/qY77N57ryWqeFxTzUj6W2pPWZMgppDuyhH/7IPBrkK8TUU2pbx8VqDhqjoqkk20OaQi8oqu+gsfGgT2fJizUHL1jsuDtxfTabD8RBLs0xn1m7dZpzzsgZWwnsPOCLCv/nHfx8wJZYRYUM8m0dZI5+7N2pZ4qDZPINXenJsewmv22WKxdVgxjJJJ6EhWMK7PjA+ujxr/EYSuSg9mR3UJ9NlgcteqhiYN/+qU8XotgJiK0Uxz8cDV7zOQmG2Mpi8HS8+UO8Ewujq/W28crsNTUYVnWwGHbMjXgHmD6jikKaI1jbiB+RtpFSCRetOUh8Q3a04wugGQ/V3cns9/hygiS2wguWbNWpBYkcmgPPrJ1r3fE0OrUumEPKBtpa86/P9p5+4DcSFZLwfIjGjnU0ly9IxAheABDMFc5727grF1WDGAs0BwmXmt7/+nbv4Dj42vBaObZTPyDnWpQe6NBDFQLP3o6eJtpdcjEplQKpOyv3QuYW0DBandiRQZfKr2IOaYR4YCWNLiuaWlgsJfr1aZIFNAeeWX8eRD0aRPTX4nu6MhbVY/ntX6k5aGHoZtSMcZRN3zNiK4QQ4jnI7AcrJVbwVqMg6WGXJyix3xHEVsSC0T8ctu6GggMfvaGiodhe2XT+hKyQbPdyniBIGjxDg1aWkYvcNl9sJbtHYB9mT8p+KNrh8mSRZvuJ7Ud74VqFKcj4DUFzLA3sotFDFGYuT1+OD44J7JX9WhLrHLBXNk0qsBJj7qL7zfWRrUGapB4WO0a9tUjfqFGTzKs5sLt/b/1mwuVhJmk1mNbzIb9rzfDcPXjUobtqWdw9OoSfuuh+sxTVHNGYwikJl+jX+mg2O/jwL3zmvn7EhAI+mnSz3gATLLm3TMfjgZhwZ8rncfdB5v7e4FnYjB+79s+2i4NoTmPHOsJ4dvCw+4d0UCO8S+KdYNFxt+A7wejvxmuJoJBBzGVr7Lg8YhKMuIFSicdW3LdDw7LdOStYUseQSCgnx22T6cDyapCAps3SVSv6xcQKFv2txJJGIMvYh7Fr/41WjbDaqF9IXIgePVQecGorWTn+diZ4J9i5SWkOeCdYgozACrtA99bdaD/+5M4zvrhyNLEYnlk71aBv/DBq39GkSebSHOHGyEgKQuxkdDgJNnNWt0eHH1917w5fWm+CBQV/OqH7Tqvbow/Wj+G2Rj/6kmyuEvgmDpYbceYe/N3x6B0Sm2ADgq/0xuizw2RNq29N/XBhJjzq7dF7lkQZ2XgZS3GIhgwff7Kf77SNV9bbrJ8OMiQyO2VCiOdYg9yv6T11zG5qd3VmIdkOjkqp1TfR1Hl3L7JzNe6miE5yPyLnN1ae9Hus6W/lvG37wTC5qXVRNUh5Ldwrm5WpI1gYzPpWLM9DtJtaIzTpoRYSTjBSgQD+Cb6rK7s6aY1qL6Q1B4nsZo9t3V8xqi3DwM7eTlJ18TlquLteCzSxWParBDSgUD7HZSdDcwjSI3QAR7JHgW+Wb7e5XSbACyLAMkUBi8m5Upoj8r6H6KHVyxvw0aS71jQO/SARBPim+Zab2+UBvCACLFMUsJicq6Q5Mt6Me2IbtzV5UwqDBpjaLx37+ViP8BuwVL7Z5napAC+IAMsUBSwm5yppDjJ3bWsYXedY741faxPmorBdJIJtwMA3x7fb3C4T4AURYJmigMXkXCnNAQDaAc1NB8ALIsAyRQGLyQHNAQAqgeamA+AFEWCZooDF5IDmAACVQHPTAfCCCLBMUcBickBzAIBKoLnpAHhBBFimKGAxOaA5AEAl0Nx0ALwgAixTFLCYHNAcAKASaG46AF4QAZYpClhMDmgOAFAJNDcdAC+IAMsUBSwmJ1tzwAEHHHDAAQcccCzjiGkOAAAAAACApQKaAwAAAACAVfD/Ab3EMZCKPzJsAAAAAElFTkSuQmCC" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">A \(\chi^2\) test was conducted to decide whether the type of drink was independent of age.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of degrees of freedom for the \(\chi^2\) test.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis for the \(\chi^2\) test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The critical value for the </span><span><span>\(\chi^2\)</span> test at the 5% significance level is 12.59. The \(\chi^2\) test statistic is calculated to be 146 with a <em>p</em>-value of 6.62 × 10<sup>−29</sup> (both numbers given correct to 3 significant figures).</span></p>
<p><span>Write down the conclusion reached at the 5 % significance level. Give a clear reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hospital collected data from <span class="s1">1000 </span>patients in four hospital wards to review the quality of its healthcare. The data, showing the number of patients who became infected during their stay in hospital, was recorded in the following table.</p>
<p class="p1" style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p class="p1">A \({\chi ^2}\)-test was performed at the <span class="s1">5% </span>significance level.</p>
<p class="p1">The critical value for this test is <span class="s1">7.815</span>.</p>
<p class="p1">The null hypothesis for the test is</p>
<p class="p1">\({{\text{H}}_0}\): Becoming infected during a stay in the hospital is independent of the ward.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the expected frequency of the patients who became infected whilst in <span class="s1">Nightingale ward.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For this test, write down the \({\chi ^2}\) statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State, giving a reason, whether the null hypothesis should be rejected.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The daily January temperature of Cairns is normally distributed with a mean of 34<span class="s1">°</span>C and a standard deviation of 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the probability that the temperature on a randomly chosen day in January is less than 39<span class="s1">°</span>C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the expected number of days in January that the temperature will be more than 39<span class="s1">°</span>C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On a randomly chosen day in January, the probability that the temperature is above \(T\) <span class="s1">°</span>C is 0.7.</p>
<p class="p1">Find the value of \(T\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following set of data which is plotted on the scatter diagram below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of the mean point \((\bar x{\text{, }}\bar y)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(r\), the Pearson’s product-moment correlation coefficient for this set of data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the regression line for \(y\) on \(x\) on the set of axes above.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The manager of a travel agency surveyed 1200 travellers. She wanted to find out whether there was a relationship between a traveller’s age and their preferred destination. The travellers were asked to complete the following survey.</p>
<p><img 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" alt></p>
<p>A \(\chi {\,^2}\) test was carried out, at the \(5\% \) significance level, on the data collected.</p>
<p>Write down the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of degrees of freedom.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The critical value of this \(\chi {\,^2}\) test is \(21.026\).</p>
<p>Use this information to write down the values of the \(\chi {\,^2}\) statistic for which the null hypothesis is rejected.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>From the travellers taking part in the survey, 285 were 61 years or older and 420 preferred Tokyo.</p>
<p>Calculate the expected number of travellers who preferred Tokyo and were 61 years or older.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A scientist measures the concentration of dissolved oxygen, in milligrams per litre (<em>y</em>) , in a river. She takes 10 readings at different temperatures, measured in degrees Celsius (<em>x</em>).</p>
<p>The results are shown in the table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>It is believed that the concentration of dissolved oxygen in the river varies linearly with the temperature.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, find Pearson’s product-moment correlation coefficient, <em>r.</em></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, find the equation of the regression line <em>y</em> on <em>x</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the equation of the regression line, estimate the concentration of dissolved oxygen in the river when the temperature is 18 °C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A survey was conducted among a random sample of people about their favourite TV show. People were classified by gender and by TV show preference (Sports, Documentary, News and Reality TV).</p>
<p>The results are shown in the contingency table below.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Find the expected number of females who prefer documentary shows.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A \({\chi ^{\,2}}\) test at the \(5\,\% \) significance level is used to determine whether TV show preference is independent of gender.</p>
<p>Write down the \(p\)-value for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following values of <em>x</em> and <em>y</em> and the scatter diagram which represents the information given in the table.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of</span></p>
<p><span>(i) <em>a</em> ;</span></p>
<p><span>(ii) <em>b</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The mean of the <em>x</em> values is 5 and the mean of the <em>y</em> values is 4. Draw the line of best fit on the scatter diagram above.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your line of best fit to estimate the value of <em>y</em> when </span><span><span><em>x</em> = </span>6.5.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The local park is used for walking dogs. The sizes of the dogs are observed at different times of the day. The table below shows the numbers of dogs present, classified by size, at three different times last Sunday.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt width="299" height="112"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write a suitable null hypothesis for a \(\chi^2\) test on this data.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(\chi^2\) for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The number of degrees of freedom is 4. Show how this value is calculated.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The critical value, at the 5% level of significance, is 9.488.</span></p>
<p><span>What conclusion can be drawn from this test? Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The lifetime, \(L\) , of light bulbs made by a company follows a normal distribution.<br>\(L\) is measured in hours. The normal distribution curve of \(L\) is shown below.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Write down the mean lifetime of the light bulbs.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The standard deviation of the lifetime of the light bulbs is \(850\) hours.</p>
<p>Find the probability that \(5000 \leqslant L \leqslant 6000\) , for a randomly chosen light bulb.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The company states that \(90\% \) of the light bulbs have a lifetime of at least \(k\) hours.</p>
<p>Find the value of \(k\) . Give your answer correct to the nearest hundred.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The weight, \(W\), of bags of rice follows a normal distribution with mean <span class="s1">1000 g </span>and standard deviation <span class="s1">4 g</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that a bag of rice chosen at random weighs between <span class="s1">990 g </span><span class="s2">and </span>1004 g<span class="s2">.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">95% </span>of the bags of rice weigh less than \(k\) grams.</p>
<p class="p1">Find the value of \(k\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For a bag of rice chosen at random, \({\text{P}}(1000 - a < W < 1000 + a) = 0.9\).</p>
<p class="p2">Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Malthouse school opens at 08:00 every morning.</p>
<p>The daily arrival times of the 500 students at Malthouse school follow a normal distribution. The mean arrival time is 52 minutes after the school opens and the standard deviation is 5 minutes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a student, chosen at random arrives at least 60 minutes after the school opens.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a student, chosen at random arrives between 45 minutes and 55 minutes after the school opens.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second school, Mulberry Park, also opens at 08:00 every morning. The arrival times of the students at this school follows exactly the same distribution as Malthouse school.</p>
<p>Given that, on one morning, 15 students arrive at least 60 minutes after the school opens, estimate the number of students at Mulberry Park school.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following scatter diagram shows the scores obtained by seven students in their mathematics test, <em>m</em>, and their physics test, <em>p</em>.</p>
<p style="text-align: left;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The mean point, M, for these data is (40, 16).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot and label the point M\(\left( {\bar m,\,\,\bar p} \right)\) on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line of best fit, by eye, on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your line of best fit, estimate the physics test score for a student with a score of 20 in their mathematics test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each day a supermarket records the midday temperature and how many cold drinks are sold on that day. The following table shows the supermarket’s data for the last 6 days. This data is also shown on a scatter diagram.</p>
<p><img 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" alt></p>
<p><img 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" alt></p>
<p>Write down</p>
<p>i) the mean temperature, \({\bar x}\) ;</p>
<p>ii) the mean number of cold drinks sold, \({\bar y}\) .</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line of best fit on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the line of best fit to estimate the number of cold drinks that are sold on a day when the midday temperature is \(10\,^\circ {\text{C}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>